I don't know Hellboy but it sounds as though Hellboy likes Liz so much that he would give his life for her (die for her)...but he's not so sure that he wants to do the dishes (wash up, do housework etc). Abe apparently likes Liz more than Hellboy does because he would give his life AND do the dishes.

Hellboy thinks of himself as a hero. He likes to do things BIG. He would die to prove he loves Liz.

But she wants him to be thoughtful and considerate. That means doing little things, too. (Anyone can tell you: the success or failure of a relationship lies in how well one does the little things.)

So Hellboy is sort of complaining that he would die for her, but she wants him to do boring things. And Abe, who has no one (at that point), says that if he had a girl like Liz, he would do the big things AND the little things.